Question

If $x{\sin }^{3}0+y{\cos }^{3}0=\sin 0\cos 0andx\sin 0=y\cos 0$ then

• A. $x^3+y^3=1$
• B. $x^2-y^2=1$
• C. $x^2+y^2=1$
• D. $x^3-y^3=1$

Answer 1

Answer: (C)

$x^2+y^2=1$

Given: $x{\sin }^{3}0+y{\cos }^{3}0=\sin 0\cos 0andx\sin 0=y\cos 0$
Now, $x{\sin }^{3}0+y{\cos }^{3}0=\sin 0\cos 0$
$x\sin 0.{\sin }^{2}30+y{\cos }^{3}0=\sin 0\cos 0$
$y\cos 0.{\sin }^{2}30+{\cos }^{3}0=\sin 0\cos 0$ (Given, $x\sin 0=y\cos 0$ )
$y\cos 0({\sin }^{2}30+{\cos }^{2}0)=\sin 0\cos 0$ (Since, $si{n}^2\theta +co{s}^2\theta =1$)
$y=\sin 0$
Similarly, $x=\cos 0$
Now, $x^2+y^2=si{n}^{2}0+co{s}^{2}0=1$ (Since, $si{n}^2\theta +co{s}^2\theta =1$)